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Artificial Intelligence (AI) has emerged in popularity recently, recording great progress in various industries. However, the environmental impact of AI is a growing concern, in terms of the energy consumption and carbon footprint of Machine Learning (ML) and Deep Learning (DL) models, making essential investigate Green AI, an attempt to reduce the climate impact of AI systems. This paper presents an assessment of different programming languages and Feature Selection (FS) methods to improve computation performance of AI focusing on Network Intrusion Detection (NID) and cyber-attack classification tasks. Experiments were conducted using five ML models - Random Forest, XGBoost, LightGBM, Multi-Layer Perceptron, and Long Short-Term Memory - implemented in four programming languages - Python, Java, R, and Rust - along with three FS methods - Information Gain, Recursive Feature Elimination, and Chi-Square. The obtained results demonstrated that FS plays an important role enhancing the computational efficiency of AI models without compromising detection accuracy, highlighting languages like Python and R, that benefit from a rich AI libraries environment. These conclusions can be useful to design efficient and sustainable AI systems that still provide a good generalization and a reliable detection., Comment: 16 pages, 9 tables, FPS 2024 conference

When a dynamical system is subject to a periodic perturbation, the averaging method can be applied to obtain an autonomous leading order `guiding system', placing the time dependence at higher orders. Recent research focused on investigating invariant structures in non-autonomous differential systems arising from hyperbolic structures in the guiding system, such as periodic orbits and invariant tori. The effect that bifurcations in the guiding system have on the original non-autonomous one has also been recently explored. This paper extends the study by providing a broader description of the dynamics that can emerge from non-hyperbolic structures of the guiding system. Specifically, we prove here that $K$-universal bifurcations in the guiding system persist in the original non-autonomous one, while non-versal bifurcations, such as the transcritical and pitchfork, do not, being instead perturbed into stable bifurcation families. We illustrate the results on examples of a fold, a transcritical, a pitchfork, and a saddle-focus. By applying these results to the physical scenario of systems with time-varying parameters, we show that the average parameter value becomes a bifurcation parameter of the averaged system.

Non-unitary $3 \times 3$ mixing matrices are present in many extensions of the Standard Model. One of the most simple extensions is the addition of $n_R$ right-handed neutrinos without imposing Lepton Number Conservation ($n_R$$\nu$SM). In the region of the parameter space where the usual seesaw approximation is valid, deviations from $3 \times 3$ unitarity of the leptonic mixing matrix are negligible, while one has three light neutrinos and two or three heavy neutrinos with masses close to the GUT scale. This gap between the mass scales occurs while having order 1 Yukawa couplings, providing a natural explanation for the smallness of light neutrino masses - hence the name seesaw. Other regions of the parameter space, with lighter heavy neutrinos - with an eV or keV mass, for instance - and bigger deviations from unitarity of the leptonic mixing matrix, are still allowed by experiment. In fact, whenever heavy neutrino masses are many orders of magnitude below the GUT scale there are interesting phenomenological implications at low energies. To analyse such regions with precision, one needs an exact parameterisation, since approximations that were valid in the usual seesaw case now fail. This thesis will consist of a study and classification of regions of the 3$\nu$SM parameter space in the light of a newly-developed exact parameterisation. Furthermore, it will also include a study of models with vector-like quarks, another simple extension of the SM, that contains a $3 \times 3$ non-unitary quark mixing matrix. Studying the most interesting regions of the parameter space of vector-like quarks models also benefits from the use of the aforementioned exact parameterisation. These regions are phenomenologically rich and may explain certain open questions like the CKM unitarity problem/Cabibbo angle anomaly. A chapter discussing the experimental implications of these models is also included., Comment: PhD Thesis, 186 pages, Abstract in English and Portuguese

Floquet's Theorem is a celebrated result in the theory of ordinary differential equations. Essentially, the theorem states that, when studying a linear differential system with $T$-periodic coefficients, we can apply a, possibly complex, $T$-periodic change of variables that transforms it into a linear system with constant coefficients. In this paper, we explore further the question of the nature of this change of variables. We state necessary and sufficient conditions for it to be real and $T$-periodic. Failing those conditions, we prove that we can still find a real change of variables that is "partially" $T$-periodic and "partially" $T$-antiperiodic. We also present applications of this new form of Floquet's Theorem to the study of the behavior of solutions of nonlinear differential systems near periodic orbits.

Important information about the dynamical structure of a differential system can be revealed by looking into its invariant compact manifolds, such as equilibria, periodic orbits, and invariant tori. This knowledge is significantly increased if asymptotic properties of the trajectories nearby such invariant manifolds can be determined. In this paper, we present a result providing sufficient conditions for the existence of invariant tori in perturbative differential systems. The regularity, convergence, and stability of such tori as well as the dynamics defined on them are also investigated. The conditions are given in terms of their so-called higher order averaged equations. This result is an extension to a wider class of differential systems of theorems due to Krylov, Bogoliubov, Mitropolsky, and Hale.

We review the theory and phenomenology of isosinglet vector-like quarks (VLQs). In recent years, interest in VLQs has been increasing, due to their contributions to new physics effects that can be tested in experiments at LHC and High-Luminosity LHC. The similarities of models with isosinglet VLQs and the seesaw framework in the leptonic sector are pointed out. The existence of VLQs leads to flavour-changing neutral currents at tree level and deviations from unitarity of the CKM matrix, introducing rich phenomenological implications. These new effects are naturally suppressed by the masses of the new quarks, that are constrained to be above the electroweak scale. In addition, striking new effects can be achieved with the inclusion of an extra complex scalar singlet. Such a minimal extension of the SM can give rise to new sources of CP violation with profound theoretical implications, allowing for a solution to the strong CP problem and a possible explanation for the baryon asymmetry of the Universe. We list and explain strong motivations to consider this class of models. We also briefly review how models with VLQs can be matched to the SM effective field theory (SMEFT). A detailed analysis of flavour observables that can be affected by the presence of VLQs is presented. Current bounds from collider searches of VLQs are summarized. We point out that the discovery of VLQs can be within the reach of present or future colliders being planned., Comment: 121 pages, 7 figures, 7 tables. Work intended as a review. Comments and references added; typos corrected. New appendix on UV completions; section 2.3 expanded. Matches version published in Physics Reports

Hilbert's 16th Problem, about the maximum number of limit cycles of planar polynomial vector fields of a given degree $m$, has been one of the most important driving forces for new developments in the qualitative theory of vector fields. Increasing the dimension, one cannot expect the existence of a finite upper bound for the number of limit cycles of, for instance, $3$D polynomial vector fields of a given degree $m$. Here, as an extension of such a problem in the $3$D space, we investigate the number of isolated invariant tori in $3$D polynomial vector fields. In this context, given a natural number $m$, we denote by $N(m)$ the upper bound for the number of isolated invariant tori of $3$D polynomial vector fields of degree $m$. Based on a recently developed averaging method for detecting invariant tori, our first main result provides a mechanism for constructing $3$D differential vector fields with a number $H$ of normally hyperbolic invariant tori from a given planar differential vector field with $H$ hyperbolic limit cycles. The strength of our mechanism in studying the number $N(m)$ lies in the fact that the constructed $3$D differential vector field is polynomial provided that the given planar differential vector field is polynomial. Accordingly, our second main result establishes a lower bound for $N(m)$ in terms of lower bounds for the number of hyperbolic limit cycles of planar polynomial vector fields of degree $[m/2]-1$. Based on this last result, we apply a methodology due to Christopher & Lloyd to show that $N(m)$ grows as fast as $m^3/128$. Finally, the above-mentioned problem is also formulated for higher dimensional polynomial vector fields.

Microservices architecture has been widely adopted to develop software systems, but some of its trade-offs are often ignored. In particular, the introduction of eventual consistency has a huge impact on the complexity of the application business logic design. Recent proposals to use transactional causal consistency in serverless computing seems promising, because it reduces the number of possible concurrent execution anomalies that can occur due to the lack of isolation. We propose an extension of the aggregate concept, the basic building block of microservices design, that is transactional causal consistent compliant. A simulator for the enriched aggregates is developed to allow the experimentation of this approach with a business logic rich system. The experiment results shown a reduction of the implementation complexity. The simulator is a publicly available reusable artifact that can be used in other experiments., Comment: 11 pages, 6 figures

Determining the existence of compact invariant manifolds is a central quest in the qualitative theory of differential equations. Singularities, periodic solutions, and invariant tori are examples of such invariant manifolds. A classical and useful result from the averaging theory relates the existence of isolated periodic solutions of non-autonomous periodic differential equations, given in a specific standard form, with the existence of simple singularities of the so-called guiding system, which is an autonomous differential equation given in terms of the first non-vanishing higher order averaged function. In this paper, we provide an analogous result for the existence of invariant tori. Namely, we show that a non-autonomous periodic differential equation, given in the standard form, has a normally hyperbolic invariant torus in the extended phase space provided that the guiding system has a hyperbolic limit cycle. We apply this result to show the existence of normally hyperbolic invariant tori in a family of jerk differential equations.

The paper describes the MetroPT data set, an outcome of a eXplainable Predictive Maintenance (XPM) project with an urban metro public transportation service in Porto, Portugal. The data was collected in 2022 that aimed to evaluate machine learning methods for online anomaly detection and failure prediction. By capturing several analogic sensor signals (pressure, temperature, current consumption), digital signals (control signals, discrete signals), and GPS information (latitude, longitude, and speed), we provide a dataset that can be easily used to evaluate online machine learning methods. This dataset contains some interesting characteristics and can be a good benchmark for predictive maintenance models.

This work analyses a class of extensions of the Standard Model through the lens of a novel exact parameterisation. This parameterisation is specially suitable to the analysis of extensions of the Standard Model with non-unitary mixing matrices, like models with vector-like fermions or right-handed neutrinos. The usefulness of this parameterisation is motivated with two example models: A) Standard Model with the addition of $n_u$ up and $n_d$ down singlet vector-like quarks and B) Standard Model with the addition of $n_R$ right-handed neutrinos., Comment: Proceedings of the Corfu Summer Institute 2021 "Workshop on the Standard Model and Beyond" August 29 - September 8, 2021, 9 pages. Typo in the 1st version: In equation 24 $Z$ should be $\overline{K}$. Versions 3 and 4: Clarified notation in the neutrino section